World Football Elo Ratings
The World Football Elo Ratings is a ranking system for men's national association football teams that is published by the website eloratings.net. It is based on the Elo rating system but includes modifications to take various football-specific variables into account, like the margin of victory, importance of a match, and home field advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for football teams. The FIFA World Rankings -not based on the Elo method- is the official national teams rating system used by the international governing body of football and is therefore more prevalent.
The ratings consider all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional.
The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula. A 2009 comparative study of eight methods found that the implementation of the Elo rating system described below had the highest predictive capability for football matches, while the men's FIFA ranking method performed poorly.
- 1 Top 60 ranking
- 2 Highest average ratings since 1970
- 3 List of number one teams
- 4 Ranking by days as leader
- 5 Elo all-time records
- 6 Averages by decade
- 7 Highest rated matches
- 8 Biggest upsets
- 9 History
- 10 Overview
- 11 Basic calculation principles
- 12 See also
- 13 Notes
- 14 References
- 15 External links
Top 60 ranking
The following table shows World Football Elo Ratings on 25 August 2016, using data from the World Football Elo Ratings web site.
Highest average ratings since 1970
Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths. The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 August 2016. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score.
List of number one teams
The following is the list of nations who have achieved the number one position in the World Football Elo Ratings since 1872:
Ranking by days as leader
|Nation||days||First Date as Leader||Last Date as Leader|
|England||11,231||30 November 1872||11 June 1988|
|Argentina||8,223||1 November 1929||Current|
|Brazil||8,104||12 June 1958||7 July 2014|
|Scotland||5,864||4 March 1876||11 March 1904|
|Germany [e]||4,284||25 July 1966||28 May 2016|
|Italy||2,713||6 June 1934||14 August 2006|
|Spain||2,495||5 September 1920||11 October 2013|
|Uruguay||2,419||25 July 1920||8 July 1931|
|Denmark||1,996||4 April 1914||20 September 1919|
|France||1,856||12 September 1984||9 July 2007|
|Hungary||1,289||25 November 1953||11 June 1958|
|Russia [f]||1,097||31 March 1963||24 June 1988|
|Netherlands||921||5 April 1920||3 July 2014|
|Austria||10||27 May 1934||5 June 1934|
|Czech Republic||8||27 June 2004||7 June 2005|
|Poland||4||11 October 1975||14 October 1975|
Elo all-time records
All-time highest ratings
The following is a list of national football teams ranked by their highest Elo score ever reached. The team in each confederation that has achieved the highest rank is shown in color.
All-time highest ranking
The following is a list of national football teams ranked by their highest Elo ranking ever reached.
Averages by decade
The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9).
Highest rated matches
A list of the 16 matches between teams with the highest combined Elo ratings (the nations' points before the matches are given).
|Nation 1||Elo 1||Nation 2||Elo 2||Score||Date||Occasion||Location|
|1||4242||Germany||2181||Argentina||2061||1 : 0 aet||2014-07-13||World Cup F||Rio de Janeiro|
|Germany||2201||Argentina||2041||2 : 4||2014-09-03||Friendly||Düsseldorf|
|3||4219||Netherlands||2104||Spain||2115||0 : 1 aet||2010-07-11||World Cup F||Johannesburg|
|4||4200||Brazil||2101||Germany||2099||1 : 7||2014-07-08||World Cup SF||Belo Horizonte|
|5||4195||Brazil||2065||Spain||2130||3 : 0||2013-06-30||Confederations Cup F||Rio de Janeiro|
|6||4191||West Germany||2002||Hungary||2189||3 : 2||1954-07-04||World Cup F||Bern|
|7||4161||Netherlands||2054||Brazil||2107||2 : 1||2010-07-02||World Cup QF||Port Elizabeth|
|8||4156||West Germany||2071||Brazil||2085||0 : 1||1973-06-16||Friendly||Berlin|
|9||4153||Brazil||2061||Netherlands||2093||0 : 0||2011-06-04||Friendly||Goiânia|
|10||4145||Hungary||2138||Brazil||2007||4 : 2||1954-06-27||World Cup QF||Bern|
|11||4141||Hungary||2167||Uruguay||1974||4 : 2||1954-06-30||World Cup SF||Lausanne|
|12||4136||Netherlands||2076||Argentina||2060||0 : 0||2014-07-09||World Cup SF||São Paulo|
|12||4136||Spain||2089||Germany||2047||1 : 0||2010-07-07||World Cup SF||Durban|
|14||4124||Brazil||2054||West Germany||2070||1 : 0||1982-03-21||Friendly||Rio de Janeiro|
|15||4115||West Germany||2082||Netherlands||2033||2 : 1||1974-07-07||World Cup F||Munich|
|16||4114||Argentina||2098||Chile||2016||0 : 0||2016-06-26||Copa América F||East Rutherford|
A list of the 15 matches with the biggest point exchange.[s] Since the importance of the match, the goal differential and the perceived home team advantage are factored in the point exchange, these are not necessarily the most surprising wins as expressed by the difference in Elo rating.[t] The nations' points before the matches are given.
|Nation 1||Elo 1||Nation 2||Elo 2||Score||Date||Occasion||Location|
|1||95||Sweden||1621||Belgium||1772||8 : 1||1924-05-29||Olympic Games||Paris|
|2||85||Fiji||1148||New Zealand||1534||4 : 0||1980-02-23||OFC Nations Cup||Nouméa|
|Czechoslovakia||1809||Argentina||1964||6 : 1||1958-06-15||World Cup||Helsingborg|
|4||84||Poland||1583||Hungary||1823||3 : 0||1936-08-05||Olympic Games||Berlin|
|5||82||Brazil||2100||Germany||2098||1 : 7||2014-07-08||World Cup||Belo Horizonte|
|6||81||Ghana||1598||Czech Republic||1975||2 : 0||2006-06-17||World Cup||Cologne|
|7||80||Khmer Republic||1200||Kuwait||1510||4 : 0||1972-05-14||Asian Cup||Bangkok|
|8||79||Paraguay||1596||Uruguay||1986||3 : 0||1929-11-01||Copa América||Buenos Aires|
|9||78||Croatia||1873||Germany||2054||3 : 0||1998-07-04||World Cup||Lyon|
|Norway||1535||Great Britain||1865||3 : 1||1920-08-28||Olympic Games||Antwerp|
|11||77||Uruguay||1785||Brazil||2125||3 : 0||1959-12-12||Copa América||Guayaquil|
|Chile||1540||Uruguay||1893||3 : 0||1937-01-10||Copa América||Buenos Aires|
|13||76||Netherlands||1962||Spain||2088||5 : 1||2014-06-13||World Cup||Salvador|
|United States||1869||Mexico||1772||0 : 5||2009-07-26||CONCACAF Gold Cup||East Rutherford|
|Germany||1851||Norway||1650||0 : 2||1936-08-07||Olympic Games||Berlin|
The Elo system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.
The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result.
The factors taken into consideration when calculating a team's new rating are:
- The team's old rating
- The considered weight of the tournament
- The goal difference of the match
- The result of the match
- The expected result of the match
The different weights of competitions in descending order are:
- World Cup Finals
- Continental championships finals and Intercontinental tournaments
- World Cup and Continental championship qualifiers
- All other tournaments
- Friendly matches
These ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional.
Basic calculation principles
The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.
The ratings change are based on the following formulae:
|= The new team rating
|= The old team rating
|= Weight index regarding the tournament of the match
|= A number from the index of goal differences
|= The result of the match
|= The expected result
|= Points Change
The number of Points Change is rounded to the nearest integer before updating the team rating.
Status of match
The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;
|Tournament or Match type||Index (K)|
|Continental Championship and Intercontinental Tournaments||50|
|World Cup and Continental qualifiers and major tournaments||40|
|All other tournaments||30|
Number of goals
The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;
If the game is a draw or is won by one goal
If the game is won by two goals
If the game is won by three or more goals
- Where N is the goal difference
Table of examples:
|Goal Difference||Coefficient of K (G)|
Result of match
W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss). This also holds when a game is won or lost on extra time. If the match is decided on penalties, however, the result of the game is considered a draw (W = 0.5).
Expected result of match
We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:
where dr equals the difference in ratings (add 100 points for the home team). So dr of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower.
The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.
Before the tournament the three teams have the following point totals.
Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:
Team A versus Team B (Team A stronger than Team B)
|Team A||Team B||Team A||Team B||Team A||Team B|
|Score||3 : 1||1 : 3||2 : 2|
Team B versus Team C (both teams approximately the same strength)
When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:
|Team B||Team C||Team B||Team C||Team B||Team C|
|Score||3 : 1||1 : 3||2 : 2|
Note that Team B loses more ranking points by losing to Team C than by losing to Team A.
- Representing West Germany from 1949 to 1990
- Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
- Combined record of the Czechoslovakian (1970-1992) and Czech national football teams (1993-present)
- Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
- Combined record of the Germany (1908-1950 & 1990-present) and West Germany (1950-1990) national football teams.
- Combined record of the Russian Empire (1912-1914), RSFSR (1923), USSR (1924-1992), CIS (1992), and Russia (1992-present) national football teams.
- as Soviet Union
- as FR of Yugoslavia
- On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
- as Zaire
- as Soviet Union
- as FR of Yugoslavia
- as Zaire
- In the 1940s, most national teams did not play games until after the end of World War II, making comparison of countries for this decade weak. For example, Mexico did not play any matches between Feb 1938 and July 1947, so that the average over the decade mostly reflects the single Elo rating achieved in February 1938
- up to 1 August 2016
- Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
- Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
- Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)
- Only matches between teams with at least 30 earlier matches each are included to allow a stabilized Elo rating. These criteria just disqualify the 4:0 Turkey:China match at the 1948 Olympic Games and the 7:1 Italy:Spain match at the 1928 Olympic Games, each with an 89 point exchange, the 3:0 Egypt:Hungary at the 1924 Olympic Games with a 80 point exchange, the 4:2 Peru:Austria at the 1936 Olympic Games with a 78 point exchange, and the 4:1 France:Mexico at the 1930 World Cup with a 76 point exchange.
- In those terms, Luxembourg featured in the two most surprising wins. First the 2:1 win over Switzerland (ER 1767) in a World Cup qualification match in September 2008 (a 762 point difference), followed by the 1:0 win vs. Czech Republic (ER 1854) in a EURO qualification match in June 1995 (a 702 point difference). These are the only wins for a team with at least 700 points less than its opponent.
- "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
- J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
- World Football Elo Ratings Eloratings.net. Retrieved: 2016-08-04.
- "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 11 August 2016. Retrieved 2016-08-11.
- Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
- Arpad Elo, Chess Life, 1962.
- About the Chessmetrics Rating System, by Jeff Sonas
- "History of the Football Union of Russia". Rfs.ru. Retrieved 2016-06-04.
- "Germany to play Argentina in September friendly". The Star. 21 March 2014. Retrieved 15 July 2014.
- Source: World Football Elo Ratings: Biggest Upsets
- Source: World Football Elo Ratings: Egypt
- Source: World Football Elo Ratings: Peru
- Source: World Football Elo Ratings: Mexico
- Source: World Football Elo Ratings: Luxembourg